Which album are you viewing, when you try to assign the location?
For me, it is working well to assign locations to multiple photos, but not, when I select the photos in Imports.
The Photos in Imports may not yet have been fully indexed in the library.
I am aways adding them first to an album, and view them all enlarged to force the download from iCloud, and only then I try to modify the locations, titles, etc.
The second problem is, that Photos tends to lose the focus on the Info.
If Photos is beeping and the cursor is losing the focus on the Info panel. If the Info is no longer in the focus of your typing, you will hear the beeping. When that happens, I restart the Mac. I have to do it a lot, after the Big Sur Upgrade.
There is another problem with entering locations in Big Sur. Currently the locations are not very precise, even when we enter precise GPS coordinates. I prefer to enter the coordinates with an Apple Script, to be sure the exact location will be used.
See: Script: Assign the Same GPS Coordinates to Several Selected Items in Photos